Other classes of reals

One way to think of the effective version of Kraft’s inequality, the so-called Kraft-Chaitin theorem, is the following.

§3. Other classes of reals. One interesting and basically unexplored class of reals is the class of d.c.e. reals. These are defined, perhaps unfortunately, as those reals a for which there exist c.e. reals and y such that a = /? — y. They are interesting since the class of c.e. reals is certainly not closed under operations such as difference. Perhaps slightly surprisingly, the d.c.e. reals form a field.